BCSSS

International Encyclopedia of Systems and Cybernetics

2nd Edition, as published by Charles François 2004 Presented by the Bertalanffy Center for the Study of Systems Science Vienna for public access.

About

The International Encyclopedia of Systems and Cybernetics was first edited and published by the system scientist Charles François in 1997. The online version that is provided here was based on the 2nd edition in 2004. It was uploaded and gifted to the center by ASC president Michael Lissack in 2019; the BCSSS purchased the rights for the re-publication of this volume in 200?. In 2018, the original editor expressed his wish to pass on the stewardship over the maintenance and further development of the encyclopedia to the Bertalanffy Center. In the future, the BCSSS seeks to further develop the encyclopedia by open collaboration within the systems sciences. Until the center has found and been able to implement an adequate technical solution for this, the static website is made accessible for the benefit of public scholarship and education.

A B C D E F G H I J K L M N O P Q R S T U V W Y Z

POINCARÉ Section 5)

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A method "of reducing the study of continuous time systems (flows) to the study of an associated discrete time system (map)" (S. WIGGINS, 1988, p.67).

J. GLEICK explains this mathematical technique as follows: "The technique reduces a three-dimensional picture to two dimensions. Each time the trajectory passes through a plane, it marks a point, and gradually a minutely detailed pattern emerges" (1987, p.143).

The same technique may be applied to more complex systems, i.e., with a higher number of initial independent conditions.

WIGGINS emphasizes: "In lower dimensional problems (say dimension < 4) numerically computed POINCARÉ maps provide an insightful and striking display of the global dynamics of a system" (p.67).

In this way, it becomes possible to gather an understandable picture of any attractor, be it common or strange. POINCARÉ's method is also related to the ergodic relation.

P. BERGÉ, Y. POMEAU and Ch. VIDAL state:

"… POINCARÉ's section leads to the replacement of the description of some evolution continuous in time by an application at discrete intervals of time."

Moreover: "… POINCARÉ's section presents the same type of topological properties as the flow of which it is born, because of its mode of construction… If the flow passes an attractor, the structural characteristics of the same will be found in the POINCARÉ section" (1984, p.67).

Thus, this method makes quite easier the study of the different types of stabilities and instabilities.

Categories

  • 1) General information
  • 2) Methodology or model
  • 3) Epistemology, ontology and semantics
  • 4) Human sciences
  • 5) Discipline oriented

Publisher

Bertalanffy Center for the Study of Systems Science(2020).

To cite this page, please use the following information:

Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]

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